Fourier Series for Singular Measures
Department of Mathematics, Butler University, Indianapolis, IN 46208, USA
Department of Mathematics, Iowa State University, 396 Carver Hall, Ames, IA 50011, USA
Author to whom correspondence should be addressed.
Academic Editors: Palle E.T. Jorgensen and Azita Mayeli
Received: 21 February 2017 / Revised: 23 March 2017 / Accepted: 24 March 2017 / Published: 28 March 2017
Using the Kaczmarz algorithm, we prove that for any singular Borel probability measure
possesses a Fourier series of the form
. We show that the coefficients
can be computed in terms of the quantities
. We also demonstrate a Shannon-type sampling theorem for functions that are in a sense
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style
Herr, J.E.; Weber, E.S. Fourier Series for Singular Measures. Axioms 2017, 6, 7.
Herr JE, Weber ES. Fourier Series for Singular Measures. Axioms. 2017; 6(2):7.
Herr, John E.; Weber, Eric S. 2017. "Fourier Series for Singular Measures." Axioms 6, no. 2: 7.
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